This method consists of two ice cream containers. The above container (for soil and plants) should be easy to stack on the below (the reservoir). The soil will not be in direct contact with the water, but as the plants grow their roots will reach the water through the holes.
For convenient indicator of water level, use a semi-transparent lower container.
Here are two examples. These also include funnels for refilling the reservoir directly, made from slim plastic bottles. These are not necessary as you can refill the reservoir by watering the soil.
Place the upper container upside down with the lid for the lower container on top (also upside down)
Then drill a bunch of holes (5-7mm drill) through the lid into the container.
(If you want a funnel) take a small plastic bottle, cut to length and glue to the inside of the upper container. Drill a hole to allow water to get to the reservoir. Here follows two examples.
Glue the bottom lid to the upper container by gluing around the sides. This seal should be watertight.
Put it on the reservoir (do not glue in place). Fill top part with soil and plant. You need to water it regularly until roots have reached the water. You can lift the upper container to check root progress. You should still water the upper container so the soil doesn't dry out completely, but the plants should be able to survive far longer without care than in a normal plant pot.
Over time you may get algae growth in the reservoir. The algae could look ugly and steal some nutrients from the water. This shouldn't be a problem for a long time, though, and when it does just empty and rinse the reservoir in the sink or shower while holding the upper container with your other hand (to protect the roots).